Guest Post by Willis Eschenbach
The canonical equation describing the energy balance of the earth looks like this:
∆Q (energy added) = ∆U (energy lost) + ∆Ocean (energy moving in/out of the ocean) (Equation 1)
This has been modified in the current climate paradigm (e.g. see Kiehl) by substituting in the following:
∆U (energy lost) = [∆T (change in surface temperature) / S (climate sensitivity)] (Equation 2)
which gives us
∆Q (energy added) = [∆T (change in surface temperature) / S (climate sensitivity)] + ∆Ocean (energy moving in/out of the ocean) (Equation 3)
As I detailed in “Where Did I Put That Energy“, the problem is that the data doesn’t bear out the substitution. In the real world, ∆U is very different from ∆T/S. There’s a whole lot of energy missing. I think that some of it is here:
Figure 1. Tracing the path of a tiny bit of energy through a simplified climate system.
Why does this count as some of the missing energy?
Note that all of the energy goes into evaporating the molecule of water. As a result, there is no net change in the surface temperature. Since the definition of the climate sensitivity is ∆T/∆Q, and ∆T is zero, that means that for this entire transaction the climate sensitivity is zero.
It is important to remember that Equation 1 is still true, and this situation complies with Equation 1. The amount of energy entering the system equals the amount leaving plus ocean storage (zero in Fig. 1). However, it does not comply with equation 2 or 3.
This certainly qualifies as a possible mechanism for the missing energy. Response time is fast, and it can move huge amounts of energy from the surface to the condensation level and eventually to space. Also, it is outside the ambit of the the climate sensitivity calculation, since the climate sensitivity for this transaction is zero.
Is this all of the missing energy? Can’t be. The missing energy is moving in huge amounts in both directions, both into and out of the system. However, the mechanism above is one-way. It can remove energy from the system, but not add energy. I say the extra energy added in the other direction comes from clouds clearing out when the temperature drops. But that is another story for another post.
My conclusion? Climate sensitivity is not a constant, it is a function of temperature. Note for example that the warmer the water, the larger a percentage of the incoming energy takes the path illustrated in Fig. 1. The formation of the clouds and thunderstorms is also temperature dependent. All of which makes the climate sensitivity strongly temperature dependent.
As always, questions, corrections, and suggestions are more than welcome.
w.
PS – Please don’t say “but you left out the greenhouse gases”. Yes, I did, but in this case they have almost no effect. The transport of the heat to the upper troposphere takes place in the thunderstorm, so it is protected from thermal exchange with the troposphere. At the top of the troposphere, where it leaves the thunderstorm, there is little atmosphere of any kind. From there it is free to radiate to space with little interference.
And in any case, GHGs will only modify rather than rule the effect. Sure, we might end up with a bit of surface warming rather than zero as in the above analysis. But the essence of the transaction is that surface temperature is not directly coupled to radiation. This means that the substitution done to get Equation 3 is not correct.
PPS — In fact, the system above does more than have zero effect on the surface temperature. When the thunderstorm starts, albedo goes up, storm winds increase evaporation, cold wind and rain from aloft chill the surface, and other cooling mechanisms kick into gear. As a result, the surface ends up cooler than when the thunderstorm started, giving negative climate sensitivity. But that is another story for another post as well.
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Lots of issues with all eqs. First off: the energy balance should look like
Energy Balance (+ or -) = [1] Energy captured from the Sun – [2] Energy emitted to space – [3] energy captured by earth (land, ocean and air) +[4] energy emitted from Earth (core heat still being depleted from Earth’s birth and the gravity forces adding energy to our molten core as we rotate the solar system and the solar system rotates the galaxy).
The balance is of where we stand (gaining or losing energy) is determined by a very complex system of systems. The simpleton and partial equations we have seen are embarrassing. For example, how much energy is captured and held by land, sea and air? There are two very large and very dynamic energy sources (external energy from the Sun and internal energy from our molten core). There are various sinks and one path for dissipation (to space). I have yet to see defensible models of all 4 factors and their error bars. Until then – no one knows.
The models assume positive feedback will multiply the CO2 caused rise by a factor of 3. Assuming positive feedback in a relatively stable system is ridiculous. My guess a couple of years ago was that negative feedback would reduce the CO2 caused rise to 1/3 of what it would be without feedbacks. That would make the IPCC and models predictions out by a factor of 9.
Could you plug my guess into your equation please. Could you use a sensitivity such that the extra incoming energy that would normally need a 1 degree rise in T to restore balance without feedback, instead only needs a 1/3 degree rise in T.
Yum. Loverly.
I’ve always favoured a water-cycle based approach put together by a software guy called Robert Clemenzi: http://qs.mc-computing.com//Global_Warming/EPA_Comments/TheGreenhouseEffect.doc
He postulates and diagrams a “heat pipe – like” effect, with the thunderstorm piercing the lower troposphere and sending energy to the escape hatch in and above the tropopause.
Willis:
This is “off topic”, yet ON TOPIC..
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790012790_1979012790.pdf
The above 373 Page report, available for download is called:
Sun, Weather and Climate.
It is full of solar wind/cosmic ray info and weather correlations from 1978.
Hope you can use it for some fuel for some future work.
Max
Why is the ‘energy’ missing? Because these people are dolts. Much like those unlikely fools that argue the missing ‘energy’ is absent from the first 2,000 feet of surface ocean but is stored in the next 13,000 feet.
It is as clear as day that during the last warming period that life forms sucked up immense amounts of CO2 and used many other biologic resources for propagation and growth. It is equally clear that the insulating effect of CO2 is hugely over-exaggerated. I would suggest that Gaea, if such a being had reason, would thank humans for releasing CO2 just at the time when it was most useful. ie, a warm period.
I’m amazaed that how much common sense , stuff that we all take for granted if we just went outside an observed weather, is finally being admitted to in the modelling. It’s obvious also that the Northern and Southern Hemispheres hold and release energy at different rates due to the land/water ratios.
Excellent post Willis. “Negative climate sensitivity”. Now there’s an incendiary term.
Chris
Norfolk, VA, USA
Even if the GHGs did cause some warming of the lower troposphere, it would only serve to
(1) increase evaporation, as described above, and
(2) make the moist warm air more ready to ascend causing convection.
The result would be to rev up this heat engine and carry energy to altitude sooner and more rapidly.
It’s a win-win for a negative feedback.
Your conclusion seems to dovetail with the one that Ferenc Miskolczi made a few years back — i.e., that the greenhouse effect has a ceiling, and that limit must have been reached already — naturally.
It is all of the common sense stuff, such as the basic water cycle Mr. (Dr.?) Eschenbach described above that the “climate scientists” want us to ignore (as they do). Instead, they want us to think that climate science is much too complicated for us (other scientists and ignorants) to understand.
vis-a-vis the missing energy.
Has anyone looked down the back of the couch?
Good post, as usual Willis.
I am keeping a low profile from the pre-Christmas noise but there is a problem that has bothered me for a while. Looking at item 2. of figure 1. Note that all of the energy goes into evaporating the molecule of water……….
The transport of the heat to the upper troposphere takes place in the thunderstorm.
Some of the heat, but all of the heat?
The assumption is that the water vapour molecule, being less dense than the surrounding atmosphere (density ratio water vapour/air @ur momisugly STP kg/m^3, 0.595/1.275) will rise, solo, and join with other consenting H2O molecules when the correct STP is reached.
But what if the water molecule released at the sea surface combines lower down in the troposphere and releases its latent heat there ? I do not mean droplet formation as in a cloud but unseen micro droplets, releasing latent heat lower down, condensing on dust particles, salt particles and dimethyl sulphide.
These nuclei are there, what is to stop this energy release lower down from the cloud base? it is hardly a pure, pristine environment from sea surface to cloud base.
Is this reasonable? It may be a source of lower atmosphere heat.
Keith Minto says:
December 23, 2010 at 10:27 pm
These nuclei are there, what is to stop this energy release lower down from the cloud base? it is hardly a pure, pristine environment from sea surface to cloud base.
Is this reasonable? It may be a source of lower atmosphere heat.
Hot air rises so the energy will go up following the storm upward motion in any case.
There was a long thread in Lucia’s and The Air Vent where a new model of wind creation is proposed by Anastassia Makarieva et al who say that condensation in addition to releasing energy creates a vacuum and winds come in to fill it up and go up, creating the large winds seen in cyclones. Not many people were convinced but in either model hot air ends up high releasing energy.
But what if the water molecule released at the sea surface combines lower down in the troposphere and releases its latent heat there ?
My reading of this is that here is just one example of where the equations do not work at all, because climate sensitivty in this case is zero. So what about the average sensitivity? Who cares?! Clearly sensitivity does change with temperature and circumstances. If models can’t even handle what happens at night and changing cloud levels an types, the model in no way represents even an “average” scenario.
Since thunderstorms are a significant pump of heat from sea surface to space in the tropics, they need to be modelled correctly. And if some of the time the sensitivity is negative? Well as Willis says, that’s another story!
If your thought experiment is correct, wouldn’t the effect of increased co2 be increased water transport rather than a hotter globe e.g. more rain and snow?
That would seem to be a net positive. At least from LA and other semi arid environs.
So is “climate sensitivity” just a way to express specific heat for the atmosphere?
I feel strongly you’re on the right track, Willis. I hope you develop your ideas fully. I think you’re agreeing with Spencer and Lindzen. Many aspects of the climate are highly non-linear. Feedback from water vapor starts out as strongly positive and ends up as strongly negative when the thunderstorms get going. But there is something else you should consider – MASS. Rising (and descending) air masses have momentum (mv) and kinetic energy (1/2mv^2). The momentum ensures that thunderstorms take time to form and run on longer than they would if air had no mass. Also, the air rises rapidly in thunderclouds and descends slowly outside of them so the kinetic energy of the air is a net carrier of energy aloft because KE is proportional to the square of the velocity. That will account for some more of your missing energy.
Non- linearity also appears in temperature because of the Stefan–Boltzmann law (sigma * T^4). Take two conditions where the average temperature is 15C (288K):
1) The temperature spends half the time at 278K and half at 298K (+/-10K).
2) The temperature spends half the time at 283K and half at 293K (+/- 5K).
The average is 288K in both cases but the LR energy emitted is different:
1) 298^4 – 278^4 = sigma * 1,913,333,760 = 107.2232239 J/s/m2
2) 293^4 – 283^4 = sigma * 955,802,880 = 53.5631934 J/s/m2
That’s a big difference. This is why all models and formulae based upon static averages are useless.
Brian H :
“heat pipe” is the best short description of what happens on a water planet when one end of the system (the surface) is heated by radiation.
anna v says:
December 23, 2010 at 10:47 pm
True, but radiative heat loss to space may be reduced if condensation in part occurs lower down, changing the equations. The condensing radiative air is caught between the sea surface and the cloud base.
I did not see the Lucia’s thread but I will check, thanks,(9mth old on my knee, thrashing!!!!)
NS 27 Nov has an article Cloud Power (p40) that has a model proposed by Quinn Brewster that suggests vapour/water phase change is radiative at least in part. (I thought it was?)
Oops. The LR energy emmited in the 2 examples are:
1) average of S *298^4 and S * 278^4 = 388.3282574 W/m2
2) average of S * 293^4 and S * 283^4 = 386.2360502 W/m2
That’s a difference of 2.09 watts
“Climate sensitivity is not a constant, it is a function of temperature”
Yes, this is probably the fundamental factor. We don’t yet seem to understand feedbacks, but this seems very plausible.
Willis, my own speculation had been that the ocean had been absorbing the heat via the thermohaline currents, however your model is provable by observation. Can you suggest an observation to prove your model?
Keith Minto says:
December 23, 2010 at 11:55 pm
What I get from your post is that you’re suggesting a non-negligible heat loss caused by condensation of water vapor in the lower troposphere, but as anna v attempted to explain, the release of energy due to condensation would warm the surrounding air, which would then continue to rise (as hot air is wont to do) following the air currents of the uncondensed water vapor.
However, some heat *is* trapped in the lower altitudes (remember, GHGs are real, water vapor *is* one, and carries most of the heat in our atmosphere, much more than the paltry amount absorbed and held by CO2), and this could be a mechanism behind it.
My question to you then, sir, is as follows. “What kind of effect would that have on the climate of Earth?” Are you suggesting some bold new form of GHG trapping? This seems actually rather inconsequential… we know that thunderstorms form, and we know they form by the travel upwards of water vapor, which then condenses and allows for heat escape to space… some of them not making it wouldn’t invalidate Willis’ argument… if you’re suggesting that’s where the “missing energy” went, then you need to brush up on the laws of thermodynamics again, because for any significant amount of energy to be lost to this mechanism would requires substantial, noticeable temperature increase in the lower troposphere (read as, Global Warming gone nuts). Furthermore, it would increase global warming not based on CO2 levels, but levels of dust and particulates in the air, things not TYPICALLY associated directly with global warming. Increased dust levels leading to higher tropical temperatures… haven’t seen the study yet.
Willis,
I think this is correct “At the top of the troposphere, where it leaves the thunderstorm, there is little atmosphere of any kind. From there it is free to radiate to space with little interference.” Not much water vapor in the stratosphere and the pressure is low so CO2 absorption lines don’t have much pressure broadening. Lacis reckons that why Mars doesn’t have strong “greenhouse” effect even though there’s lots and lots and LOTS of CO2.
anna v, I reckon the onset of convection and inrushing air at the surface gaining rotation and causing tropical cyclones is indisputable. Rising air causes low pressure at the surface just as subsiding air causes high pressure at the surface. What the heck do these people think causes dust devils, tornados and cyclones?????
Some of these people need to get out more and start flying around in the atmosphere for a few years.
Perhaps I’m being thick, but I don’t think equations 1 and 2 contradict.
What you seem to have is a very simplified model where dQ in = dQ out, with dT = 0.
So dO = dT / S = 0/S = 0.
For no energy lost, eq 2 becomes 0 = 0 / S
Which by my reading means sensitivity is irrelevant in this simple model, not that it is 0.